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Fluctuation and Noise Letters

ENTANGLEMENT DEGRADATION IN A STRING OF ATOMS COUPLED BY THE ELECTROMAGNETIC FIELD

Péter Földi, M. G. Benedict, Tamás Serényi, Attila Czirják

Published Sep 1, 2004• 1 citation
Publisher

Abstract

We investigate the dynamics of short linear chains consisting of two-level systems (atoms) coupled by the electromagnetic field. The environment of photon modes acts as a source of noise and leads to the disappearance of the initially present multipartite entanglement. The rate of this process (entanglement degradation) depends on the separation of the atoms, and also on the initial state. With the aid of the appropriate entanglement witnesses we show that this rate is exceptionally low for the so-called subradiant states. Below one resonant wavelength of atomic separation the effect of the environmental noise is weaker than the dipole-dipole interaction and multipartite entanglement can be formed in the initial stage of the time evolution.

DOI
10.1142/s0219477504002105

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We investigate the dynamics of short linear chains consisting of two-level systems (atoms) coupled by the electromagnetic field. The environment of photon modes acts as a source of noise and leads to the disappearance of the initially present multipartite entanglement. The rate of this process (entanglement degradation) depends on the separation of the atoms, and also on the initial state. With the aid of the appropriate entanglement witnesses we show that this rate is exceptionally low for the so-called subradiant states. Below one resonant wavelength of atomic separation the effect of the environmental noise is weaker than the dipole-dipole interaction and multipartite entanglement can be formed in the initial stage of the time evolution.
We investigate the dynamics of short linear chains consisting of two-level systems (atoms) coupled by the electromagnetic field. The environment of photon modes acts as a source of noise and leads to the disappearance of the initially present multipartite entanglement. The rate of this process (entanglement degradation) depends on the separation of the atoms, and also on the initial state. By the aid of the appropriate entanglement witnesses we show that this rate is exceptionally low for the so-called subradiant states. Below one resonant wavelength of atomic separation the effect of the environmental noise is weaker than the dipole-dipole interaction and multipartite entanglement can be formed in the initial stage of the time evolution.
The time evolution of short linear chains consisting of dipole coupled two-level systems (atoms) is investigated under the influence of oscillator modes, which represent the environment. The dynamics of the system is calculated using the super-radiant master equation. The focus is on phenomena related to the environment induced decoherence and entanglement degradation. For large atomic distances the initially present pair entanglement is destroyed independently from the spatial position of the two atoms, while when the distance between the atoms becomes comparable to the resonant wavelength the rate of entanglement degradation corresponds to the strength of the pair interaction. Below one resonant wavelength of atomic separation, formation of pair entanglement is also possible in the initial stage of the time evolution. In this case it is found that pair entanglement is formed and destroyed periodically, and the strengths of the consecutive ‘entanglement revivals’ are damped depending on the initial state. The subradiant states, for which decoherence is slow, also preserve pair entanglements for an exceptionally long time.
A model containing two two-level atoms and a single-mode cavity is considered, and the effect of the time-dependent atom-field couplings on entanglement between the two atoms is studied. The results indicate that both for one-photon processes and for two-photon processes, the disappearance of the initial entanglement is delayed due to the linear modulation of the atom-field coupling coefficients as compared to the constant coupling model. The delayed time of the disappearance of the initial entanglement for the two-photon processes is much longer than that for the one-photon processes in the case of adiabatic variation.
We analyze the time evolution of quantum entanglement in a model consisting of two two-level atoms interacting with a two-mode electromagnetic field for a variety of initial states. We study two different coupling schemes motivated by the forms that can arise due to atomic separation. We observe a variety of qualitative features such as entanglement sudden death, dynamical generation, protection, and transfer between subsystems. Our quantitative analysis shows that these cases with different couplings and initial states differ significantly in these qualitative features. The multifarious behaviors in these two-mode cases suggest the importance of considering atomic separation carefully for any model where two atoms interact with a common field.
We consider two two-level atoms, interacting with two independent dissipative cavities, each of which is driven by an external source. The two cavity fields are both initially prepared in the coherent states, and the two two-level atoms are initially prepared in the singlet state |Ψ − ⟩ = (|eg⟩ – |ge⟩)/√2. We investigate the influence of the damping constant κ, the intensity of the external sources F, and the relative difference of the atomic couplings r on the entanglement between the two atoms. In the dispersive approximation, we find that the entanglement between the two atoms decreases with the time evolution, and the decreasing rate of entanglement depends on the values of F/κ, κ/ω, and r. For the given small values of F/κ and κ/ω, on the one hand, the increasing of r favors entanglement decreasing of the atomic system, on the other hand, when r → 1 the entanglement decreasing becomes slower. With the increasing of the value of κ/ω, the influence of r on the decreasing rate of entanglement becomes smaller, and gradually disappears for the big value of κ/ω.
We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole-dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole-dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.